What is the value of sin((19pi)/(12))-sin(pi/(12)) ?

The value of sin((19pi)/(12))-sin(pi/(12)) is -sqrt(3/2)

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sin((19pi)/(12))-sin(pi/(12))

sin (\frac{19 π}{12}) - sin (\frac{π}{12})

- \frac{3}{2}

Solution steps

sin (\frac{19 π}{12}) - sin (\frac{π}{12})

Rewrite using trig identities:

2 sin (\frac{3 π}{4}) cos (\frac{5 π}{6})

= 2 sin (\frac{3 π}{4}) cos (\frac{5 π}{6})

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

Use the following trivial identity:

cos (\frac{5 π}{6}) = - \frac{3}{2}

= 2 \cdot \frac{2}{2} (- \frac{3}{2})

Simplify

2 \cdot \frac{2}{2} (- \frac{3}{2}) : - \frac{3}{2}

= - \frac{3}{2}

csc (\frac{2}{3})

cos (- \frac{13 π}{4})

8 sin (3 5^{\circ})

\frac{sin ( π )}{cos ( π )}

4 cos (2 (\frac{3 π}{2}))

What is the value of sin((19pi)/(12))-sin(pi/(12)) ?
The value of sin((19pi)/(12))-sin(pi/(12)) is -sqrt(3/2)